Which of the following functions are solutions of the differential equation y'' + y = sin(x)?a) y= sinxb) y= cosx
c) y=1/2sinx
d) -1/2xcosx
Answers
Answer:
Option (d)
Step-by-step explanation:
Given,
y" +y=sin x ...........(1)
The particular solution
Putting the value of y" and y in equation (1)
Therefore 2A =0 -2B=1
⇒A=0
Therefore
Final answer:
The solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).
Explanation:
To determine which of the given functions are solutions of the differential equation y'' + y = sin(x), we can substitute each function into the equation and check if it satisfies the equation. Let's go through each option:
- Substituting y = sin(x) into the equation, we get -sin(x) + sin(x) = sin(x), which is not true. So, y = sin(x) is not a solution.
- Substituting y = cos(x) into the equation, we get -cos(x) + cos(x) = sin(x), which is true. So, y = cos(x) is a solution.
- Substituting y = (1/2)sin(x) into the equation, we get -(1/2)sin(x) + (1/2)sin(x) = sin(x), which is true. So, y = (1/2)sin(x) is a solution.
- Substituting y = -(1/2)xcos(x) into the equation, we get (-1/2)xcos(x) + (1/2)xcos(x) = sin(x), which is true. So, y = -(1/2)xcos(x) is a solution.
Therefore, the solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).
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Step-by-step explanation:
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To find out how much flour Ricky needs, we first need to find 1 1/2 times the amount of flour in the original recipe.
2 3/3 cups of flour is the same as 8/3 cups of flour.
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To find out how much flour Ricky needs, we can multiply this amount by 1 1/2:
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